## emcrazy14 3 years ago Differentiate; x^2/(1+x)^2

1. ajprincess

This is of the form u/v. (u/v)'=(u'v-v'u)/v^2 Here u=x^2 and v=(1+x)^2. (x^n)'=nx^(n-1) Can u do it @emcrazy14?

2. emcrazy14

I got the answer -2x/(1+x)^3. Is it correct?

3. experimentX

differentiate: 1/(1/x + 1)^2

4. ajprincess

check the sign @emcrazy14. It shud be 2x/(1+x)^3

5. emcrazy14

Ok, thanks. Do I multiply (x+1) with a negative sign to change it into (1+x) so that it cancels with the the denominator (1+x)^4?

6. experimentX

just ask the wolf for differentiation Question.

7. ajprincess

nope. (x+1)=(1+x)

8. emcrazy14

Then how oes it become +2x? :O

9. emcrazy14

@experimentX : wolf? :O *does

10. experimentX
11. ajprincess

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12. experimentX

$x^2/(1+x)^2 = 1/(1/x + 1)^2 = ({1 \over x} + 1)^{-2}$ use chain rule ... this should be shorter.

13. emcrazy14

@ajprincess : Get it now. Thank you so much! :D

14. ajprincess

welcome:) @experimentX's method is much more simpler. U can use that too.:)

15. emcrazy14

@experimentX : Once I perfect this one, I'll use the one you mentioned. Thank you! :)